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Question number: 64

Question

A small asteroid is orbiting around the sun in a circular orbit of radius r0 with speed V0. A rocket is launched from the asteroid with speed V = αV0, where V0 is the speed relative to the sun. The highest value of α for which the rocket will remain bound to the solar system is (ignoring gravity due to the asteroid and effects of other planets) –

Choices

Choice (4)

Response

a.

Equation

b.

Equation

c.

1

d.

Equation

Question number: 65

Question

A liquid drop placed on a horizontal plane has a near spherical shape (slightly flattened due to gravity). Let R be the radius of its largest horizontal section. A small disturbance causes the drop to vibrate with frequency ν about its equilibrium shape. By dimensional analysis the ratio Equation can be (here σ is surface tension, ρ is density, g is acceleration due to gravity, and k is an arbitrary dimensionless constant)

Choices

Choice (4)

Response

a.

Equation

b.

Equation

c.

Equation

d.

Equation

Question number: 66

Question

Jet aircrafts fly at altitudes above 30, 000 ft where the air is very cold at – 400C and the pressure is 0.28 atm. The cabin is maintained at 1 atm pressure by means of a compressor which exchanges air from outside adiabatically. In order to have a comfortable cabin temperature of 250C, we will require in addition

Choices

Choice (4)

Response

a.

A heater to warm the air injected into the cabin

b.

An air-conditioner to cool the air injected into the cabin

c.

Neither a heater nor an air-conditioner; the compressor is sufficient

d.

Alternatively heating and cooling in the two halves of the compressor cycle